混合地理加权回归模型的空间异方差性检验  

Spatial Heteroscedasticity Test for Mixed Geographically Weighted Regression Models

作　　者：古丽斯坦·库尔班尼牙孜 张丽平 田茂再[1,2,3] GULISTAN·Kurbanyaz;ZHANG Li-ping;TIAN Mao-zai(School Of Statistics And Data Science,Xinjiang University of Finance and Economics,Urumqi 830046,China;Center for Applied Statistics,Renmin University of China,Beijing 1008721,China;School of Statistics,Renmin University of China,Beijing 1008721,China)

机构地区：[1]新疆财经大学统计与数据科学学院,新疆乌鲁木齐830012 [2]中国人民大学应用统计科学研究中心,北京100872 [3]中国人民大学统计学院,北京100872

出　　处：《数理统计与管理》2024年第5期761-775,共15页Journal of Applied Statistics and Management

基　　金：教育部人文社科科学基金(21XJJA910001);国家自然科学基金(11861042);国家自然科学基金(71864034);新疆维吾尔自治区自然科学基金青年项目(2024D01B16)。

摘　　要：混合地理加权回归模型中一个常用的假设是随机误差项为同方差,然而实际问题中同方差性假设不一定成立。本文基于混合地理加权回归模型的残差平方和与残差绝对值,分别构造了两种空间异方差性检验统计量。通过蒙特卡洛数据模拟对两种统计量的控制第一类错误的能力和检验的功效进行评价。数据模拟结果表明,两种检验统计量在检测空间异方差性方面具有较好的准确性和可靠性,相比之下基于残差绝对值的检验统计量能给出更精确的检验结果,而且对不同的误差分布具有较强的稳健性。进一步,我们通过实际数据分析,验证了本文提出的两种检验统计量的有效性与实际应用,并给出了最后的结论。In mixed geographically weighted regression models,there has been a common assumption of homoscedasticity.In many practical situations,however,the assumption may not be true.In this paper,we propose two test statistics for detecting spatial heteroscedasticity for mixed geographically weighted regression models based on the sum of squares of residuals and the absolute value of residuals respectively.Monte Carlo data simulation experiments are conducted to evaluate the performance of the proposed two methods in the ability to control type I errors and the power of the tests.Data simulation results show that the two test statistics have good accuracy and reliability in detecting spatial heteroscedasticity,especially the test statistics based on the absolute value of residuals can give more accurate test results,and have strong robustness to different error distributions.Furthermore,through the analysis of actual data,we verify the effectiveness and practical application of the two test statistics proposed in this paper,and givethe final conclusion.

关 键 词：混合地理加权回归模型 空间异方差性 检验统计量 

分 类 号：O212[理学—概率论与数理统计] O212.7[理学—数学]